monad
A monad over a category^{} $\mathcal{C}$ is a triple $(T,\eta ,\mu )$, where $T$ is an endofunctor of $\mathcal{C}$, $\eta $ is a natural transformation from the identity functor on $\mathcal{C}$, and $\mu $ is a natural transformations from $T\circ T$ to $T$, such that the following two properties hold:

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$\mu \circ (\mu \circ T)\equiv \mu \circ (T\circ \mu )$

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$\mu \circ (T\circ \eta )\equiv {\mathrm{id}}_{\mathcal{C}}\equiv \mu \circ (\eta \circ T)$
These laws are illustrated in the following diagrams.
